2013

Journal Articles/ Conference Proposals

An Examination of Proving using a Problem-solving Framework(2013) Proceedings of the 16th Annual Conference on Research in Undergraduate Mathematics Education

I presented this paper and the results within it at the 2013 RUME conference. It describes a mathematician and a graduate student and how they differed in their proving of the same theorem, both with respect to each other and with respect to a problem-solving framework created by Carlson and Bloom (2005). Both the proposal and the final RUME conference paper is located below.

Dissertation

Proof and Proving: Logic, Impasses, and the Relationship to Problem Solving(2013) New Mexico State University

My doctoral dissertation included the work with logic and impasses below, along with new findings about how the problem-solving process and the proving process coincide. In the logic chapters, I also discuss "proof frameworks," a term coined by Selden and Selden as the part of a proof that can be done without much knowledge of the mathematics of the theorem to be proved. All is explained thoroughly in the dissertation.

Conference Presentations/Invited Talks

At Saint Joseph's, I was invited by Dr. Tetyana Berezovski to give a talk to a group of Philadelphia mathematics educators. The talk, done partly with Math Snacks and partly with my impasses results, is below:

This was a special colloquium talk, considering that this is my alma mater and I return to show my results from research and Ph.D dissertation. This talk included two of my three dissertation topics, and can be downloaded below:

In this conference, I presented on the third portion of my dissertation: my examination of proving using a problem solving framework developed by Carlson and Bloom (2005). You can download my presentation slides and my full paper below: